Question: I have a multi-stage testing procedure using items drawn from a pre-calibrated item bank. Each stage gives each person a measure and standard error. Can I combine these measures to give each person an overall measure?
Answer: The most exact answer would be to use all of a person's responses to all stages to estimate a new measure - but this may not be practical. Typically the first-stage is a short, wide subtest. The later stages may be narrower, longer subtests. So raw score performance and measurement precision can vary greatly between the subtests. RMT 8:3 p. 376, suggests that a useful combined measure is obtained by standard error weighting the subtest measures:
If it is reasonable to think of all subtests as measuring this same fixed effect, then its standard error approximates 1 / sqrt( Σ ( 1 / SE subtest ² ) ).
Summing multiple measures. J.M. Linacre 17:2 p. 925
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